Physics of Light

Achievement Standard 90768
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Reflection

Light travels in straight lines. If you look down a short length of hose, you can only see the end if it is straight. Light will either bend, reflect or be absorbed when it hits something.
All reflected rays obey the law of reflection: the angle of reflection is equal to the angle of incidence.

Plane mirrors
This means a 'flat' mirror like the ordinary one you see on a wall. It also applies to things like reflections in a pond.

The reflected rays 'look like' they have come from behind the mirror - if you shine a torch onto another person you see in a mirror, they se the 'you' in the mirror shining the torch at them.
By applying the law of reflection to at least two imaginary rays of light from a point (A in diagram), we can see where its image (A' in diagram) is. This image is formed at the point where the reflected rays intersect - in this case, the 'virtual rays', which are the apparent rays behind the mirror where the reflected rays appear to have come from. If you were to repeat the process for all of the corners of the triangle above, you would get the image shown. You would quickly see that it is the same size, way up, and distance from the mirror as the object, but it is the other way around (the spiral on it curls in the opposite direction). We say that it is reversed (in sense).

Curved mirrors

1. Concave mirrors
Curved mirrors can be concave or convex. They are formed from a section of a sphere.
The diagram below shows a section through a 'theoretical' concave mirror.


Definitions: The centre of the sphere is called the centre of curvature, c. The centre of the mirror is called the pole. The line connecting c and the pole is called the principal axis, Halfway along the principal axis between the pole and c is the principal focus, f. The distance across the mirror is called the aperture.
Rays of light travelling in particular ways with reference to these points behave in certain, predictable ways.

1. any ray travelling parallel to the principal axis will be reflected through f
2. any ray passing through f will be reflected parallel to the principal axis
3. any ray passing through c will be reflected back along its own path.

These are illustrated below:







The reason for the last is obvious - it is a radius line, and thus the angle of incidence is zero. The reason for the other two is a little less obvious, but relates to the mathematics of small angles. Both of these rules regarding the focus are approximations - they would only be true if the angle from the centre of curvature is small. If the aperture of the mirror is too large, the rays no longer behave in exactly this way and you get something called spherical abberation. For a mirror to be optically true, the focal length divided by the aperture (the 'f-ratio') must be quite large. If the aperture is large, the mirror shape needs to change from spherical to parabolic (you should know from maths that a parabola is close to circular near its turning point). A similar principle applies to lenses, and is important in photography (for further information, read this Wikipedia entry on f-ratio)

Ray diagrams in concave mirrors
The fact that the rays described above behave predictably can be used to draw 'ray diagrams' in order to find the image of objects without having to do a lot of maths or measure angles of incidence with a protractor.
When we do this, we draw the mirror as a flat plane with a little concave curve in it to indicate what type of mirror it is. This avoids spherical abberation.
In the diagram below, a small 'test object' has been placed beyond c and two rays from the end of the arrow have been drawn to see how they behave under reflection.


We can see that these rays intersect again where shown on the diagram, and from this infer where the image is (red arrow). We can now describe the image. Certain terms are used to do this:
The image can be

• Erect (the right way up) or inverted (upside down)
• Enlarged (bigger), reduced (smaller) or the same size
• Normal (same way around) or reversed (back to front)
• an image is either real or virtual. The image behind a plane mirror is virtual – there are no real rays of light there. A real image can be formed on a screen. All real images are inverted.

From this, we can see that the image above is real, reduced and inverted.
If we try this exercise with test objects in different positions with a concave mirror, a pattern emerges:

Position of object	Position of image	Type of image
beyond c	between f and c	real, reduced, inverted
at c	at	real same size, inverted
between f and c	beyond c	real, enlarged, inverted
between f and pole	behind mirror	virtual, enlarged, erect

There is no image if the object is placed at the focus. These same rules apply to convex lenses.

Convex mirror:
The focus and centre of curvature of a convex mirror are behind the mirror. The rules for reflection of rays parallel to the principal axis are the same as for concave mirrors, but the focus is behind the mirror:




As with concave mirrors, these rays can be used to construct a ray diagram to find the image of an objcect:


Refraction:
Refraction means the bending of light when it travels from one transparent medium to another e.g. air to water, water to glass and so on.
Light travels at different speeds in different transparent substances. It is fastest in a vacuum, where it travels at 300,000 km per second
(or 3 x 108 m s-1). This is the fastest possible speed; NOTHING can go faster than this.
Light travels at about 200,000 km/s in glass. The ratio of the speed of light in a vacuum to that in a substance is called the refractive index. So the refractive index of glass is 300,000 km s-1/200,000 km s-1 = 1.5
Note that there are no units in this answer, because they cancel out. It is a dimensionless quantity.
It is the change of speed of the light that causes it to refract, or bend.

The reason for the change in speed causing the light to bend is a little easier to visualize when you use a wave model for light:



Have a go at a Learning object on refraction here (needs username and password; SHC students - your username and password is the same as the one for Brittanica Online)

Lenses
Lenses produce images by refraction rather than reflection. A lens refracts light rays or waves to a point called a focus:
A lens that brings waves to a focus as shown on the left is called a converging lens. All converging lenses are thicker at the centre than they are at the edges, but they can be a variety of shapes.

Note that the lenses illustrated above will only act as converging lenses is they are placed into a medium with a refractive index lower than that of the lens. If they were placed into a medium of greater refractive index, they would become diverging. For example, a convex bubble of air in glass acts as a diverging, not converging lens.


Ray diagrams for lenses:
A similar set of rules applies for 'special rays' to those you use for mirrors..

• a ray travelling parallel to the principal axis will be refracted through the focus
• a ray passing through the focus wil be refracted parallel to the principal axis
• a ray passing through the pole will not be refracted

Note that the last rule is different from the mirror rules. The lens surfaces at the pole are parallel, so it is just like a window. You could use the ray passing through 2f (the equivalent of c on a mirror) - it will be refracted through the 2f on the other side of the lens. However, n drawing diagrams for lenses you will rarely need to do this.
Images are produced in similar locations to those from mirrors. For example, an object between f and 2f will produce an image beyond 2f which is real, enlarged and inverted as shown below;


An object between f and the pole produces a virtual image. Note that with lenses, virtual images are on the same side of the lens as the object. You will need to draw in virtual rays and construction lines.


When drawing ray diagrams for diverging lenses, remember to use the appropriate focus. Keep in mind which way the rays will bend - away from the focus. You will need to draw in the virtual rays.


Spherical abberation: as with mirrors, if the rays are a long way from the principal axis they will not be refracted exactly through the focus. This is called spherical abberation, and is a problem for very 'thick' lenses. For example, people with very thick glasses see the edge of their field of vision distorted (curved) as a result of this.Click here for diagram and further explanation.

Total internal reflection
When light rays go from a medium of higher to lower refractive index e.g. water to air, glass to water, the rays are refracted away from the normal.
This means that there is some angle for which the angle of refraction is 90 degrees - ray Q in the diagram below:

Imagine we have a light source on the bottom of a pool of water as illustrated above. The rays are refracted as shown (yellow rays). However, ray Q is refracted along the surface. It is said to be incident at the critical angle.
Ray R is incident at greater than the critical angle. It is reflected back inside the water, not refracted. This is called total internal refection, Unlike reflection in a mirror, 100% of the light energy is reflected (the reflection you see of yourself in a window at night s called partial reflection).
You can see total internal reflection on the surface of a pool, as shown in the photo to the right.
The critical angle depends on the refractive index (or optical density) of the substance. Diamonds have the highest refractive index of any natural substance (at 2.4), so they have a very small critical angle. This is what makes diamonds 'sparkle'.
Optical fibres rely on total internal reflection to 'bounce' light along their length, acting as a 'light pipe'. The light can be reflected thousands of times - the only limit is the transparency of the glass from which the fibre is made.

Colour
What our eyes see as colour is actually different wavelengths of light. Light can be thought of as a type of wave, a wave made of electric and magnetic force fields.

Red light has the longest wavelength that we can see at about 670 nanometres (one nanometre is 10-9m). Blue is the shortest we can see at about 540 nm. This is called the visible spectrum.

click for source

The diagram above shows the colours of the visible spectrum; the numbers below it are the wavelength of the light in units called nanometres (1 nm = 1 millionth of a millimetre)

White light is a mixture of different wavelengths from the visible spectrum. Each wavelength refracts slightly differently, so that if you shine white light through a prism, the different colours emerge at different angles.

This is called dispersion. A rainbow is caused because the sun’s rays are internally reflected, but emerge at an angle to their original path, causing dispersion. Example question
We only see the colours dispersed like this when the light shines through two non-parallel surfaces, as the dispersion cancels out if the two surfaces are parallel. This is why you don't see the light through a window dispersed. Dispersion is a problem at the edge of thick lenses because the edges are not parallel. Good quality cameras have an array of differently shaped lenses to overcome this problem.

We can see a mixture of red, green and blue light as white. By varying the proportion of these three colours, you can produce most of the colours we see. This is how colour tv works; it is called additive colour. The diagram to the right shows what would happen if three equally intense and overlapping cirles of light were shone on a white screen (it isn't meant to be purple around the outside; some quirk of the software). When your TV or computer screen looks yellow, there are no yellow dots.Look closely at the yellow area on the right, and you will see that the red and green dots are glowing brightly. A program like Photoshop or the Gimp lets you set a colour by adjusting the value of each of red, green and blue (RGB) from zero to 255 (maximum brightness), producing a possible 256x256x256, or about 16 million colours. In the diagram to the right, each circle has a value of 255 for its respective colour i.e. the yellow is 255-255-0 for RGB.

Colour printing works because white paper reflects all colours in equal amounts. Inks filter out the other colours; for example, blue ink absorbs red and green light and transmits the blue light reflected from the paper. To achieve a good range of colours, three colours of ink are used: cyan (blue) magenta (pink) and yellow. In theory, this can produce all colours, but in practice black ink is used to get better blacks, and to make black and white printing easier. This is called subtractive colour (sometimes known as CMYK colour after the four colurs - K stands for black). Converting RGB values to CMYK was once quite a difficult software task.

Colour filters for stage and other lights work the same way - by removing the other colours from white light. This means that a red filter blocks green and blue light and lets red through only. In theory, a green shirt viewed under such red light should appear black.
Light of a single colour is termed monochromatic. It is difficult to produce monochromatic light using filters, and requires expensive and high quality printers. Laser light is always monochromatic, and the light from red LEDs is pretty close. The light from low pressure sodium lamps is also monochromatic (low pressure sodium are the really orange looking street lights, the paler orange ones are high pressure sodium lights which contain some other colours as well).